Sliding mode control of a class of Itô type distributed parameter systems with delay

Luo, Qi; Deng, Fujin; Jun-dong, Bao; Zhao, Biao

doi:10.1016/s0252-9602(07)60006-x

Cited by 4 publications

(6 citation statements)

References 10 publications

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“…The construction of control law is very tricky, and the method is direct. This is different from the previous work in SMC for other distribution systems, which use matrix splitting technique [19,23,34] or direct design of discontinuous control law [24,25]. Their methods are suitable for those system, which is difficult to build equivalent control and can be utilized to deal with complex model.…”

Section: Sliding Mode Areamentioning

confidence: 82%

“…Both sliding mode equation and control law are established by using the equivalent control. This is different from the previous work in SMC of other distribution systems, which use matrix splitting technique [19,23,34] or direct design of discontinuous control law [24,25]. (iii) There is no existing specialized software suited for synchronization of reactiondiffusion Hopfield neural networks with s-delays.…”

Section: Introductionmentioning

confidence: 81%

“…For instance, integral sliding surface is a reasonable alternative for linear sliding surface. Unfortunately, after a scrutiny scan into published results on SMC for distributed systems, we find that the linear sliding surface is still the only option in selecting switching surface due to its distinct structure [1,13,19,25]. So exploiting nonlinear sliding surface is one of our research direction in the future.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…So exploiting nonlinear sliding surface is one of our research direction in the future. The splitting technique will also be discussed for the design of SMC for distributed systems in the future work [19]. By the way, the noise is unavoidable in the real world [14,15], so synchronization of stochastic reaction diffusion HNNs with s-delays will be considered in the next work.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…SMC is considered as a potential approach in synchronization of HNNs, which is a discontinuous control. Its main advantages are fast response, good transient performance, and robustness to external disturbance [1,19,23,25,29,33,34]. A great volume of the literature has been published on the theory and application of SMC for various systems [25,33].…”

Section: Introductionmentioning

confidence: 99%

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Synchronization of reaction–diffusion Hopfield neural networks with s-delays through sliding mode control

Liang

Wang

et al. 2022

NAMC

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Synchronization of reaction–diffusion Hopfield neural networks with s-delays via sliding mode control (SMC) is investigated in this paper. To begin with, the system is studied in an abstract Hilbert space C([–r; 0];U) rather than usual Euclid space Rn. Then we prove that the state vector of the drive system synchronizes to that of the response system on the switching surface, which relies on equivalent control. Furthermore, we prove that switching surface is the sliding mode area under SMC. Moreover, SMC controller can also force with any initial state to reach the switching surface within finite time, and the approximating time estimate is given explicitly. These criteria are easy to check and have less restrictions, so they can provide solid theoretical guidance for practical design in the future. Three different novel Lyapunov–Krasovskii functionals are used in corresponding proofs. Meanwhile, some inequalities such as Young inequality, Cauchy inequality,Poincaré inequality, Hanalay inequality are applied in these proofs. Finally, an example is given to illustrate the availability of our theoretical result, and the simulation is also carried out based on Runge–Kutta–Chebyshev method through Matlab.

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Section: Sliding Mode Areamentioning

confidence: 82%

Section: Introductionmentioning

confidence: 81%

Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Synchronization of reaction–diffusion Hopfield neural networks with s-delays through sliding mode control

Liang

Wang

et al. 2022

NAMC

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Transitional processes in linear stochastic parabolic and hyperbolic systems with constant delays

Полосков

2021

29th Russian Conference on Mathematical Modelling in Natural Sciences

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Stability Analysis for Stochastic Markovian JumpReaction‐Diffusion Neural Networks with Partially Known TransitionProbabilities and Mixed Time Delays

Zhang

Naizheng

2012

Discrete Dynamics in Nature and Society

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The stability problem is proposed for a new class of stochastic Markovian jump reaction-diffusion neural networks with partial information on transition probability and mixed time delays. The new stability conditions are established in terms of linear matrix inequalities (LMIs). To reduce the conservatism of the stability conditions, an improved Lyapunov-Krasovskii functional and free-connection weighting matrices are introduced. The obtained results are dependent on delays and the measure of the space AND, therefore, have less conservativeness than delay-independent and space-independent ones. An example is given to show the effectiveness of the obtained results.

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Sliding mode control of a class of Itô type distributed parameter systems with delay

Cited by 4 publications

References 10 publications

Synchronization of reaction–diffusion Hopfield neural networks with s-delays through sliding mode control

Synchronization of reaction–diffusion Hopfield neural networks with s-delays through sliding mode control

Transitional processes in linear stochastic parabolic and hyperbolic systems with constant delays

Stability Analysis for Stochastic Markovian JumpReaction‐Diffusion Neural Networks with Partially Known TransitionProbabilities and Mixed Time Delays

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